The rms value of emf is given by $E=(8 \sin \omega t+6 \cos \omega t)$ volt is
The rms value of emf is given by $E=(8 \sin \omega t+6 \cos \omega t)$ volt is
- $5 \sqrt{2} \mathrm{~V}$
- $7 \sqrt{2} \mathrm{~V}$
- 10 V
- $10 \sqrt{2} \mathrm{~V}$
Solution
$
\begin{aligned}
E=(8 \sin \omega t & +6 \cos \omega t) \\
& =(A \cos \theta \sin \omega t-A \sin \theta \cos \omega t)
\end{aligned}
$
where, $A \cos \theta=8$ and $A \sin \theta=6$.
$
\begin{aligned}
A^2\left(\cos ^2 \theta+\sin ^2 \theta\right) & =8^2+6^2=100 \\
A & =10 \\
\text { rms value, } E_{\mathrm{rms}} & =\frac{A}{\sqrt{2}}=\frac{10}{\sqrt{2}}=\frac{5 \times 2}{\sqrt{2}}=5 \sqrt{2}
\end{aligned}
$
Asked in: AP EAMCET 2018 (23 Apr Shift 1)
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